We consider the issue of analysing complex ecological data in the presence of covariate information. Several issues can arise when analysing such data, not least the need to take into account where there are missing covariate values. This is most acutely observed in the presence of time-varying covariates. We consider data collected in the form of capture-recapture data, where the corresponding recapture probabilities are less than unity, so that individuals are not always observed at each capture event. This often leads to a large amount of missing time-varying individual covariate information, since the covariate cannot usually be recorded if an individual is not observed. We consider a Bayesian approach, where we are able to deal with large amounts of missing data, by essentially treating the missing values as auxiliary variables. This approach also allows a quantitative comparison of different models via posterior model probabilities, obtained via the reversible jump Markov chain Monte Carlo algorithm. To demonstrate this approach we analyse data relating to Soay sheep, which pose several statistical challenges in fully describing the intricacies of the system.
Bayesian approach; Covariate information; Missing data; Model discrimination; Reversible jump Markov chain Monte Carlo; Soay sheep.